Hello,
Such small bumps on the limbs can be due to keratosis pilaris. Keratosis pilaris occurs when the human body produces excess keratin, a natural protein in the skin. There is currently no known cure for keratosis pilaris, however, there are effective treatments available which make its symptoms less apparent. Treatment includes tretinoin or Triamcinolone cream or Adapalene, a retinoid medication. Exfoliation, intensive moisturizing creams, creams and lotions containing alpha hydroxy acids and urea may be used to temporarily improve the appearance and texture of affected skin.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
There's many conditions that can cause bumps, Keratosis pilaris is a good canidate, I suggest using lotions and cleansers, if push comes to shove and you hate how they look you could try Tretinoin lotion.
Good luck